| 非局部弹性直杆振动特征及Eringen常数的一个上限 |
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| 引用本文： | 郑长良.非局部弹性直杆振动特征及Eringen常数的一个上限[J].力学学报,2005,37(6):796-798. |
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| 作者姓名： | 郑长良 |
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| 作者单位： | 大连海事大学机电与材料工程学院 |
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| 摘 要： | 应用非局部连续介质理论推导了弹性直杆的振动方程，并采用分离变量法
进行求解，得到了振动方程的本征方程、模态函数及通解. 结果表明：非局部连续介质弹性
直杆的自振频率因非局部效应而降低，降低的幅度不仅与材料内禀长度相关，还与振动频率
的阶次相关；而且频率大小存在极限值，显示了与晶格点阵相同特性. 通过与Brillouin格
波结果比较，给出了Eringen非局部理论中材料常数的一个上限.
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| 关 键 词： | 非局部理论 弹性直杆 自振频率 材料常数 上限 |
| 文章编号： | 0459-1879(2005)06-0796-03 |
| 收稿时间： | 2004-05-19 |
| 修稿时间： | 2005-08-02 |
The free vibration characteristics of nonlocal continuum bar and a boundary of material constant in Eringen's nonlocal model |
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| Zheng Changliang.The free vibration characteristics of nonlocal continuum bar and a boundary of material constant in Eringen''s nonlocal model[J].chinese journal of theoretical and applied mechanics,2005,37(6):796-798. |
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| Authors: | Zheng Changliang |
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| Abstract: | The dynamic equation of nonlocal elastic bar based on nonlocal continuum theory is derived and solved using variable separating technique. The eigenequation, mode functions and general solution of nonlocal elastic bar are obtained. Solutions show that nonlocal effects decrease the eigenfrequency and the decrease depends on not only the internal characteristic length but also the order of frequency. And there exists a limitation value for all the eigenfrequencies, which is similar to the result of lattice dynamics. Compared the limit value with Brillouin's solution of lattice dynamics, an upper bound for material constant in Eringen's nonlocal theory is given. |
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| Keywords: | nonlocal continuum theory elastic bar free vibration frequency material constant upper bound |
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